How do you roll a ball from the inside?
First, let’s look at the bottom of BB-8. It’s a sphere that can roll. So, how do you make a sphere roll without pushing it? This one isn’t so difficult. All you need is a moveable mass inside the sphere. Maybe this mass is a tiny car with wheels (on the inside of the sphere) or maybe it’s a hamster. Either way, when the mass moves up the wall of the sphere a little bit, the center of mass for the whole sphere shifts.

When the center of mass shifts away from being vertically over the contact point, there is an external torque on the sphere. This torque then increases the angular momentum of the sphere and causes it to roll. Once the sphere starts rolling, the inside mass could just stay at the lowest point—except there is some external friction which will require the inside mass to continue to ride up the side and provide some torque.

But wait? Can you really make the ball roll from the inside? Wouldn’t that be like lifting yourself up by pulling on your belt? It might sort of seem that way, but it’s actually different. If you wanted to lift yourself up from your belt, there would be no external force on you except for the gravitational force pulling you down. When the inside mass moves up the wall, there is an external force to accelerate the sphere horizontally—friction. Here is a more detailed image showing all the forces on the sphere when the mass moves up the wall.